Search results for "Analisi matematica"

MR2817222 Ursescu, Corneliu, A mean value inequality for multifunctions. Bull. Math. Soc. Sci. Math. Roumanie (N.S.) 54(102) (2011), no. 2, 193–200

2011

The paper is devoted to extend some mean value inequalities from the function setting to the multifunction one. Let (M,d) be a metric space, let F be a multifunctions defined on D \subset R and taking values in the family of nonempty subsets of M, and let g: D\rightarrow R be a strictly increasing function. The author proves the following inequality: \frac{\delta(F(b),F(a))}{g(b)-g(a)} \leq \sup_{s\in [a,b)\cap D} \sup_{S\in F(s)} \sup_{t\in (s,b)\cap D} \frac{\delta(F(t),S)}{g(t)-g(s)}, where a and b are two points of D with a<b and, if Q and P are nonempty subsets of M, then \delta(Q,P)=\sup_{p\in P} \inf_{q\in Q}d(q,p). An application of the previous inequality to the Dini derivatives of…

Multimeasures and integration of multifunctions in Banach spaces

2014

(p,2)-equations resonant at any variational eigenvalue

2018

We consider nonlinear elliptic Dirichlet problems driven by the sum of a p-Laplacian and a Laplacian (a (p,2) -equation). The reaction term at ±∞ is resonant with respect to any variational eigenvalue of the p-Laplacian. We prove two multiplicity theorems for such equations.

Global representation and multiscale expansion for the Dirichlet problem in a domain with a small hole close to the boundary

2019

For each pair (Formula presented.) of positive parameters, we define a perforated domain (Formula presented.) by making a small hole of size (Formula presented.) in an open regular subset (Formula presented.) of (Formula presented.) ((Formula presented.)). The hole is situated at distance (Formula presented.) from the outer boundary (Formula presented.) of the domain. Thus, when (Formula presented.) both the size of the hole and its distance from (Formula presented.) tend to zero, but the size shrinks faster than the distance. Next, we consider a Dirichlet problem for the Laplace equation in the perforated domain (Formula presented.) and we denote its solution by (Formula presented.) Our ai…

On multivalued weakly Picard operators in partial Hausdorff metric spaces

2015

We discuss multivalued weakly Picard operators on partial Hausdorff metric spaces. First, we obtain Kikkawa-Suzuki type fixed point theorems for a new type of generalized contractive conditions. Then, we prove data dependence of a fixed points set theorem. Finally, we present sufficient conditions for well-posedness of a fixed point problem. Our results generalize, complement and extend classical theorems in metric and partial metric spaces.

SOME EXAMPLES RELATED TO A CLASS OF FUNCTIONALS WITHOUT GLOBAL MINIMA

2012

Abstract: In this paper, we provide six examples which show the sharpness of the assumptions of a recent deep result of Ricceri about a class of functionals without global minima.

Non-homogeneous Dirichlet problems with concave-convex reaction

2022

The variational methods are adopted for establishing the existence of at least two nontrivial solutions for a Dirichlet problem driven by a non-homogeneous differential operator of p-Laplacian type. A large class of nonlinear terms is considered, covering the concave-convex case. In particular, two positive solutions to the problem are obtained under a (p -1)-superlinear growth at infinity, provided that a behaviour less than (p -1)-linear of the nonlinear term in a suitable set is requested.

Solutions with sign information for nonlinear Robin problems with no growth restriction on reaction

2019

We consider a parametric nonlinear Robin problem driven by a nonhomogeneous differential operator. The reaction is a Carathéodory function which is only locally defined (that is, the hypotheses concern only its behaviour near zero). The conditions on the reaction are minimal. Using variational tools together with truncation, perturbation and comparison techniques and critical groups, we show that for all small values of the parameter λ &gt; 0, the problem has at least three nontrivial smooth solutions, two of constant sign and the third nodal.

MR3157399 Reviewed: Kesavan, S. Continuous functions that are nowhere differentiable. Math. Newsl. 24 (2013), no. 3, 49–52. (54C05)

2014

The author uses the Baire category theorem to prove the existence of nowhere differentiable functions in C([0,1]). Precisely, the author proves the following: Theorem 1. There exist continuous functions on the interval [0,1] which are nowhere differentiable. In fact, the collection of all such functions forms a dense subset of C([0,1]).

Common fixed points in ordered Banach spaces

2008

In this paper we introduce the notion of g-weak isotone mappings in an ordered Banach space and we extend some common fixed point theorems of Dhage, O’Regan and Agarwal